We study the properties of supernova (SN) driven interstellar turbulence with a numerical magnetohydrodynamic (MHD) model. Calculations were done using the RIEMANN framework for MHD, which is highly suited for astrophysical flows because it tracks shocks using a Riemann solver and ensures pressure positivity and a divergence-free magnetic field. We start our simulations with a uniform density threaded by a uniform magnetic field. A simplified radiative cooling curve and a constant heating rate are also included. In this radiatively-cooling magnetized medium, we explode SNe one at a time at randomly chosen positions with SN explosion rates equal to and 12 times higher than the Galactic value. The evolution of the system is basically determined by the input energy of SN explosions and the output energy of radiative cooling. We follow the simulations to the point where the total energy of the system, as well as thermal, kinetic, and magnetic energy individually, has reached a quasi-stationary value. From the numerical experiments, we find that: i) both thermal and dynamical processes are important in determining the phases of the interstellar medium, and ii) the power index n of the $B-p^n$ relation is consistent with observed values.